Methods and apparatus for optical communications via pulse amplitude modulation (PAM) in dense wavelength-division multiplexing (DWDM) systems

ABSTRACT

A method includes applying, to a modulated digital signal, a forward error correction (FEC) including a low-density parity-check (LDPC) to produce a coded digital signal. Nyquist shaping is applied to the coded digital signal to generate a filtered digital signal. A representation of the filtered digital signal is transmitted in an optical communication channel via a dense wavelength division multiplexing (DWDM) scheme.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.17/132,449, now U.S. Pat. No. 11,177,888, filed Dec. 23, 2020, which isa continuation of U.S. patent application Ser. No. 16/456,761, now U.S.Pat. No. 10,903,910, filed Jun. 28, 2019, and entitled “Methods andApparatus for Optical Communications Via Pulse Amplitude Modulation(PAM) in Dense Wavelength-Division Multiplexing (DWDM) Systems,” whichis a non-provisional of and claims priority under 35 U.S.C. § 119 toU.S. provisional application No. 62/840,619, filed Apr. 30, 2019, andentitled “Methods and Apparatus for Optical Communications Via PulseAmplitude Modulation (PAM) in Dense Wavelength-Division Multiplexing(DWDM) Systems,” the disclosure of each of which is incorporated hereinby reference in its entirety.

FIELD

One or more embodiments relate to apparatus and methods of opticalcommunications via pulse amplitude modulation (PAM).

BACKGROUND

Coherent optical communications can employ a variety of spectrallyefficient modulation formats, such as M-ary phase-shift keying andquadrature-amplitude modulation (QAM), relying upon stable carrier-phaseestimation in the digital domain. The phase information of signals incoherent optical communications is also preserved after detection,thereby allowing equalizing linear transmission impairments via digitalsignal processing (DSP). As a result, coherent optical communicationscan achieve high capacity and are considered a promising technology formodern data center networks. Coherent optical communications, however,also suffer from several drawbacks, including high cost, high powerconsumption, and implementation complexity.

Pulse amplitude modulation (PAM), in contrast, does not involve coherentdetection and therefore has low cost, low power consumption, andrelatively straightforward implementation. To fully explore thepotential of PAM in data center networks, however, a few challengesremain to overcome. For example, the coarse entropy granularity ofexisting M-PAM (M=2, 4, 8, etc.) is usually not sufficient to meet thedynamic bandwidth demands. In addition, a large capacity gap also existsbetween uniform M-QAM/PAM formats and the Shannon limit. Furthermore,the low spectral efficiency of the intensity modulation/direct detection(IM/DD) solution can restrict the throughput of the modern densewavelength division multiplexing (DWDM) data center networks.

SUMMARY

Some embodiments described herein relate generally to opticalcommunications via pulse amplitude modulation (PAM), and, in particular,to methods and apparatus for optical communications via PAM and Nyquistshaping in dense wavelength division multiplexing (DWDM) systems. Insome embodiments, a method includes applying, to a modulated digitalsignal, a forward error correction (FEC) including a low-densityparity-check (LDPC) to produce a coded digital signal. Nyquist shapingis applied to the coded digital signal to generate a filtered digitalsignal. A representation of the filtered digital signal is transmittedin an optical communication channel via a dense wavelength divisionmultiplexing (DWDM) scheme.

In some embodiments, an apparatus includes an encoder configured toapply a FEC to a modulated digital signal to generate a coded digitalsignal. The apparatus also includes a digital filter operatively coupledto the encoder and configured to apply Nyquist shaping to the codeddigital signal to generate a filtered digital signal. The apparatus alsoincludes a digital to analog converter (DAC) operatively coupled to thedigital filter, where the DAC is configured to send a representation ofthe filtered digital signal into an optical communication channel.

In some embodiments, a non-transitory computer readable storage mediumstores data representing software executable by a computer, the softwareincluding instruction to apply, to a modulated digital signal, a FEC toproduce a coded digital signal. The software further includesinstruction to apply Nyquist shaping to the coded digital signal togenerate a filtered digital signal. The software further includesinstruction to transmit a representation of the filtered digital signalin an optical communication channel via a DWDM scheme.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings primarily are for illustration purposes and are notintended to limit the scope of the subject matter described herein. Thedrawings are not necessarily to scale; in some instances, variousaspects of the subject matter disclosed herein may be shown exaggeratedor enlarged in the drawings to facilitate an understanding of differentfeatures. In the drawings, like reference characters generally refer tolike features (e.g., functionally similar and/or structurally similarelements).

FIG. 1 shows a flowchart illustrating a method of optical communicationvia pulse amplitude modulation (PAM), according to an embodiment.

FIGS. 2A and 2B show frequency responses of two Nyquist filters havingan ROF of 1 and 0.1, respectively, according to an embodiment.

FIGS. 3A and 3B show distribution functions of constellation points in auniform PAM-8 scheme and an exponential PAM-8 scheme, respectively,according to an embodiment.

FIG. 4 shows a schematic of an apparatus for optical communication viaPAM, according to an embodiment.

FIG. 5 shows a schematic of a transceiver for optical communication viaprobabilistic shaping (PS) PAM, according to an embodiment.

FIG. 6 shows a schematic of a system for optical communication via PSPAM, according to an embodiment.

FIG. 7 shows bit error rate (BER) as a function of optical signal tonoise ratio (OSNR) under different transmission configurations,according to an embodiment.

FIG. 8 shows BER as a function of OSNR in optical communications viaPAM-8 using different PS schemes, according to an embodiment.

FIG. 9 shows BERs of optical communications as a function ofsignal-to-noise ratio (SNR) using different code rates of low-densityparity-check (LDPC) codes, according to an embodiment.

FIGS. 10A-10C show frequency responses of neighboring wavelengthdivision multiplexing (WDM) channels using different roll-off factors(ROFs) of Nyquist shaping over the neighboring channels, according to anembodiment.

FIGS. 11A and 11B show BER performances at different ROFs usingLDPC-coded uniform distribution and PS distribution, respectively,according to an embodiment.

DETAILED DESCRIPTION

In some embodiments, a method includes modulating a digital signal viapulse amplitude modulation (PAM) followed by applying Nyquist shaping tothe digital signal to generate a filtered digital signal. The filtereddigital signal is then converted into an analog signal for transmissionin an optical communication channel via a dense wavelength divisionmultiplexing (DWDM) scheme. The Nyquist shaping can improve the spectralefficiency (e.g., decrease the spacing between adjacent wavelengths inDWDM) and reduce inter-channel crosstalk of the optical communicationchannel. As a result, Nyquist shaping can decrease the bandwidth usedfor transmitting a given signal or equivalently increase the capacity ofa given channel.

Conventionally, in intensity modulation/direct detection (IM/DD)systems, spectral efficiency was not regarded by the industry as animportant factor, given that the total channel capacity is less than 1Tb/s in most cases. In other words, few wavelength channels with largechannel spacing were used, so the industry didn't have to reduce thesignal bandwidth. In data center networks, however, the demand forbandwidth is usually very high. Coherent communications may offer thebandwidth, but the cost and power consumption can be prohibitive.Inventors herein realize the promising potential of PAM based IM/DDsolutions to provide a great trade-off between capacity, cost, powerconsumption, and footprint. In this solution for large capacitycommunication, more wavelength channels are used and Nyquist shaping nowis employed to reduce inter-channel crosstalk.

In some embodiments, the PAM includes an N-ary PAM, where N is aninteger equal to or greater than 4. For example, the PAM can be PAM-4,PAM-8, or even higher order PAMs.

In some embodiments, the Nyquist shaping is implemented by a digitalfilter, such as a square-root raised cosine filter or a raised cosinefilter. The digital filter can have a roll-off factor (ROF) adjustablebetween 0 and 1. In some embodiments, the ROF of the digital factorduring use can be substantially equal to or less than 0.5.

In some embodiments, before applying the Nyquist shaping, the digitalsignal undergoes probabilistic shaping, such as a Maxwell-Boltzmanndistribution or an exponential distribution. The probabilistic shapingcan be performed by a distribution matcher (DM), which can change thenumber of bits per symbol in the digital signal (also referred to asentropy).

In some embodiments, a forward error correction (FEC) code is applied tothe digital signal after the probabilistic shaping and before theNyquist shaping. In some implementations, the FEC includes a low-densityparity-check (LDPC) code. The FEC can be implemented by an encoder at anadjustable code rate (e.g., between 0 and 1).

In some embodiments, the digital signal is processed within atransceiver (e.g., Nyquist shaping, probabilistic shaping, and FEC), andone or more properties of the optical communication channel are measuredand employed to adjust operations of the transceiver that sends theanalog signal. For example, an OSNR monitor can be used to measure theoptical signal to noise ratio (OSNR) or chromatic dispersion level ofthe optical communication channel. Based on the measurement, thetransceiver can change one or more of its operation parameters,including the ROF of the Nyquist shaping, the code rate of the FEC, andthe number of bits per symbol in probabilistic shaping. In this manner,the different processing mechanisms (e.g., Nyquist shaping,probabilistic shaping, and FEC) can be systematically optimized.

FIG. 1 shows a flowchart illustrating a method 100 of opticalcommunication via pulse amplitude modulation (PAM), according to anembodiment. The method 100 includes, at 110, modulating a digital signalvia PAM, such as PAM-4, PAM-8, or higher order PAMs. At 120, Nyquistshaping (also referred to as Nyquist pulse shaping or NPS) is applied tothe modulated digital signal to generate a filtered digital signal. Themethod 100 also includes, at 130, converting the filtered digital signalinto an analog signal and transmitting the analog signal, at 140, in anoptical communication channel via a DWDM scheme.

As described herein, the Nyquist shaping at 120 can improve the spectralefficiency and reduce inter-channel crosstalk or inter-symbolinterference (ISI) in optical communications. For example, Nyquistshaping can provide an almost rectangular shape frequency response andtherefore reduce the channel spacing.

In some embodiments, the Nyquist shaping can be implemented by a digitalfilter such as a raised-cosine (RC) filter. Without being bound by anyparticular theory or mode of operation, the frequency response of a RCfilter can be written as:

$\begin{matrix}{{H_{RC}(\omega)} = \left\{ \begin{matrix}T_{S} & {0 \leq {❘\omega ❘} < {{\pi\left( {1 - {ROF}} \right)}/T_{S}}} \\{{\frac{T_{S}}{2}\left( {1 - {\sin\left\lbrack {\frac{T_{S}}{2 \times {ROF}}\left( {{❘\omega ❘} - \frac{\pi}{T_{S}}} \right)} \right\rbrack}} \right)},} & {{{\pi\left( {1 - {ROF}} \right)}/T_{S}} \leq {❘\omega ❘} < {{\pi\left( {1 + {ROF}} \right)}/T_{S}}} \\0 & {{❘\omega ❘} > {{\pi\left( {1 + {ROF}} \right)}/T_{S}}}\end{matrix} \right.} & (1)\end{matrix}$where ROF is the roll-off factor (ROF) of the RC filter, co is theangular frequency, and T_(S) is the symbol duration. In someembodiments, the Nyquist shaping can be implemented by a square-rootraised cosine (SRRC) filter, and the frequency response of an SRRCfilter can be written as H_(SRRC)(ω)=√{square root over (H)}_(RC)(ω).

In some embodiments, the ROF of the digital filter implementing theNyquist shaping is adjustable (e.g., between 0 and 1, with ROF=1indicating no Nyquist shaping and ROF=0 indicating the strongestshaping). Generally, a smaller ROF can provide a frequency response thatis closer to a square shape and therefore tends to allow for reducedchannel spacing. On the other hand, however, a smaller ROF may alsoincrease the memory length and complexity in constructing the digitalfilter. In some embodiments, the ROF used in the method 100 can besubstantially equal to or less than 0.5 (e.g., about 0.5, about 0.4,about 0.3, about 0.2, about 0.1, or less, including any values and subranges in between).

In some embodiments, the Nyquist shaping is implemented in electricaldomain, i.e., the Nyquist shaping is applied to the digital signalbefore the digital signal is converted into the analog signal. Inelectrical domain, it is generally more convenient to generate anarbitrary ROF so as to optimize (or improve) the transmission of thesystem. In some embodiments, the Nyquist shaping can be implemented inoptical domain, i.e., the Nyquist shaping is applied to the opticalsignal after the digital to analog conversion.

FIGS. 2A and 2B show frequency responses of two SRRC Nyquist filtershaving an ROF of 1 and 0.1, respectively, according to an embodiment. Asseen in FIG. 2B, the digital filter with ROF=0.1 has a nearly squarefrequency response. In contrast, the digital filter having an ROF=1 asshown in FIG. 2A provides little shaping to incident pulses.

In some embodiments, the method 100 further includes applyingprobabilistic shaping (PS) to the digital signal before the Nyquistshaping. In probabilistic shaping, symbols having lower amplitudes aretransmitted with a higher probability, thereby decreasing the totalpower consumption (i.e., more power efficient). In addition,probabilistic shaping can also decrease the sensitivity to noise andtherefore increase the channel capacity and reduce the gap to Shannonlimit.

Several distribution schemes can be employed to apply the probabilisticshaping to the digital signal. In some deployments, the probabilisticshaping can be applied using a Maxwell-Boltzmann (MB) distribution. ForMB distribution, the transmission probability of each constellationpoint α_(i) can be written as:

$\begin{matrix}{{{P\left( a_{i} \right)} = {{\exp\left( {{- \lambda}{a_{i}}^{2}} \right)}/{Z(\lambda)}}},{\lambda \geq 0}} & (2)\end{matrix}$where λ is a scaling factor that is employed to adjust the entropy ofthe signal.

In some deployments, the probabilistic shaping can be applied using anexponential distribution. Exponential distribution can be suitable forintensity modulation with direct detection (IM/DD) schemes. In thisscheme, the transmission probability of each constellation point α_(i)can be written as:

$\begin{matrix}{{{P\left( a_{i} \right)} = {{\exp\left( {{- \lambda}{a_{i}}} \right)}/{Z(\lambda)}}},{\lambda \geq 0}} & (3)\end{matrix}$In both Equations (2) and (3), the function Z(λ) is employed tonormalize the probability (i.e., ensure that the sum of probabilities ofall constellation points in a symbol is one). The normalization functionZ(λ) can be defined as:

$\begin{matrix}{{{Z(\lambda)} = {\sum\limits_{i}{\exp\left( {{- \lambda}{a_{i}}^{2}} \right)}}},{\lambda \geq 0}} & (4)\end{matrix}$

FIGS. 3A and 3B show the distribution functions of constellation pointsin a uniform PAM-8 scheme and an exponential PAM-8 scheme, respectively,as a function of optical signal amplitude according to an embodiment. Ascan be seen in FIG. 3B, as the amplitude of the constellation pointincreases, the transmission probability of the constellation pointdecreases exponentially.

In some embodiments, the method 100 also includes applying a forwarderror correction (FEC) code to the digital signal (e.g., before theNyquist shaping at 120 and after the probabilistic shaping). In somedeployments, the FEC includes a hard decision FEC, in which thecorresponding receiver decides between 1 or 0 depending on whether thereceived signal level is above or below a certain threshold level, i.e.,the decision rules are based on only two levels 0 and 1. In somedeployments, the FEC includes a soft decision FEC, in which the receivertakes into account an additional confidence factor to decide between 1and 0. For example, the confidence factor can be measured by thedistance between the signal level and 1 or 0, and this approach canresult in an additional coding gain of about 1 to 2 db and accordinglyan overall improvement of about 20% to 40% for distance reachability(i.e., the distance of communication).

In some embodiments, the FEC includes a low-density parity-check (LDPC)code, which is a linear error correcting code that can transmit amessage over a noisy transmission channel. LDPC codes arecapacity-approaching codes and allow the noise threshold to be close tothe Shannon limit. As a result, the combination of PS distribution andLDPC code can significantly improve the reliability of the resultingoptical communication. In some embodiments, the FEC is implemented by anencoder having an adjustable code rate. The encoder can adjust the coderate based at least in part on the status of the optical communicationchannel.

In some embodiments, the method 100 also includes monitoring anattribute of the optical communication channel during transmission ofthe analog signal and adjusting the operation of the transceiver basedat least in part on the measured attribute. In some deployments, themethod 100 measures the OSNR of the optical communication channel usingan in-service, in-band, real-time optical signal to noise ratio (OSNR)monitor. When the measured OSNR is satisfactory (e.g., above a givenpredefined value or preset value), the transceiver can then decrease theROF of the digital filter applying the Nyquist shaping so as to decreasethe bandwidth used for transmitting the analog signal. Accordingly, morewavelength channels can be established within the optical communicationchannel, thereby increasing the aggregate capacity of the opticalcommunication channel.

In some deployments, the transceiver can also increase the code rate ofthe FEC in response to the OSNR being greater than a given value. Insome deployments, the transceiver can increase the number of bits persymbol during probabilistic shaping. These adjustments can similarlyincrease the aggregate capacity of the optical communication channel.

In some deployments, in response to the OSNR being greater than a givenvalue, the transceiver can make more than one adjustment so as tooptimize (or improve) the system performance. For example, thetransceiver can decrease the ROF and increase the FEC code rate. Inanother example, the transceiver can increase the number of bits persymbol and decrease the ROF. Any other combination of adjustments canalso be employed.

In some deployments, in response to the measured OSNR being below agiven value, the transceiver can make one or more of the followingadjustments: increasing the ROF during Nyquist shaping, decreasing theFEC code rate, and/or decreasing the number of bits per symbol.

In some implementations, the method 100 includes measuring the chromaticdispersion level of the optical communication channel and then adjustingthe operation of the digital filter, the DM, and/or the encoder based onthe measured chromatic dispersion level. In some embodiments, inresponse to the chromatic dispersion level being greater than apreselected threshold value, the transceiver can decrease the ROF duringNyquist shaping, decrease the FEC code rate, and/or decrease the numberof bits per symbol. In some deployments, in response to the chromaticdispersion level being less than a threshold value, the transceiver canincrease the ROF during Nyquist shaping, increase the FEC code rate,and/or increase the number of bits per symbol.

FIG. 4 shows a schematic of an apparatus 400 for optical communicationvia PAM, according to an embodiment. The apparatus 400 (e.g., atransmitter, or a transceiver) includes a modulator 410 configured toencode binary data into a digital signal PAM, such as PAM-4, PAM-8, orhigher order PAMs. A digital filter 420 is operatively coupled to themodulator 410 and configured to apply Nyquist shaping to the digitalsignal. The apparatus 400 also includes a digital to analog converter(DAC) 430 operatively coupled to the modulator 410 and the digitalfilter 420. The DAC 430 is configured to convert the digital signal toan analog signal and send the analog signal into an opticalcommunication channel 440 (e.g., an optical fiber) using a densewavelength division multiplexing (DWDM) scheme.

In some implementations, the digital filter 420 includes raised cosinefilter. In some implementations, the digital filter 420 includes asquare-root raised cosine filter. In some implementations, the ROF ofthe digital filter 420 is adjustable. In some implementations, thedigital filter 420 is configured to apply the Nyquist shaping at aroll-off factor (ROF) substantially equal to or less than 0.5.

In some implementations, the apparatus 400 further includes a DM (notshown in FIG. 4 ; see, e.g., FIG. 5 and FIG. 6 ) operatively coupled tothe modulator 410. The DM is configured to apply probabilistic shapingto the digital signal before the digital filter 420 (e.g., the DM can beplaced between the modulator 410 and the digital filter 420). In someimplementations, the probabilistic shaping includes a Maxwell-Boltzmanndistribution or an exponential distribution.

In some implementations, the apparatus 400 further includes an encoder(not shown in FIG. 4 ; see, e.g., FIG. 5 and FIG. 6 ) operativelycoupled to the modulator 410. The encoder is configured to apply alow-density parity-check (LDPC) code to the digital signal before thedigital filter 420 (e.g., the encoder can be disposed between themodulator 410 and the digital filter 420).

As shown in FIG. 4 , the apparatus 400 further includes a controller 450operatively coupled to the digital filter 420. The controller 450 isconfigured to receive information representing an optical signal tonoise ratio (OSNR) or a chromatic dispersion level of the opticalcommunication channel 440 measured during transmission of the analogsignal. Based at least in part on the received information, thecontroller 450 can control the digital filter 420 to change the ROF ofthe Nyquist shaping. For example, when the OSNR is greater than apredefined or preselected threshold value, the controller 450 cancontrol the digital filter 420 to decrease the ROF so as to increase theaggregate capacity of the optical communication channel 440. In anotherexample, in response to the chromatic dispersion level greater than apredefined or preselected threshold value, the controller 450 cancontrol the digital filter 420 to decrease the ROF.

In some implementations, the controller 450 is configured to control theDM to change the number of bits per symbol in response to the receivedinformation about the optical communication channel 440. For example, inresponse to the OSNR being greater than a predefined or preselectedthreshold value, the controller 450 can control the DM to increase thenumber of bits per symbol. In another example, in response to thechromatic dispersion level greater than a predefined or preselectedthreshold value, the controller 450 can control the DM to decrease thenumber of bits per symbol.

In some embodiments, the controller 450 is configured to control theencoder to change the code rate of the FEC in response to the receivedinformation about the optical communication channel 440. For example, inresponse to the OSNR being greater than a predefined or preselectedthreshold value, the controller 450 can control the encoder to increasethe FEC code rate. In another example, in response to the chromaticdispersion level greater than a predefined or preselected thresholdvalue, the controller 450 can control the encoder to decrease the FECcode rate.

FIG. 5 shows a schematic of an apparatus 500 for optical communicationvia PS PAM, according to an embodiment. The apparatus 500 includes a DM510 to receive a digital signal 501 modulated in a PAM scheme and toapply probabilistic shaping to the digital signal 501. As describedherein, the probabilistic shaping can include a Maxwell-Boltzmanndistribution or an exponential distribution. In addition, the DM 510 isalso configured to change the number of bits per symbol depending on thestatus of the optical communication channel.

A bit labeler 520 is operatively coupled to the DM 510 to constrain (orcontrol) bits of the digital signal for a particular property. In a PAMsignal, a signal constellation usually provides a set of possiblesymbols that are to be transmitted, and the symbols correspond tocodewords output from an encoder. In some embodiments, the bit labelingincludes gray-code labeling, in which neighboring signal points differin exactly one bit position.

The apparatus 500 also includes an encoder 530 operatively coupled tothe bit labeler 520 so as to apply forward error correction (FEC) to thedigital signal after bit labeling. As described herein, the encoder 530can adjust the FEC code rate in response to the status of the opticalcommunication channel. After the encoder 530, a PAM mapper 540 isconfigured to map bits into symbols for the digital signal.

A digital filter 550 is operatively coupled to the PAM mapper 540 andemployed to apply Nyquist shaping to the digital signal after the PAMmapper 540. The digital filter 550 has an adjustable ROF and isconfigured to change the ROF of the Nyquist shaping in response to thestatus of the optical communication channel. An optical modulator 560 isoperatively coupled to the digital filter 550 to convert the digitalsignal into an optical signal for subsequent transmission.

FIG. 6 shows a schematic of a system 600 for optical communication viaPS PAM, according to an embodiment. The system 600 includes a firsttransceiver 610, a second transceiver 620, a fiber channel 640 foroptical communication between the first transceiver 610 and the secondtransceiver 620, and a monitor 630 to monitor the status of the fiberchannel 640. For illustrative purposes only, the first transceiver 610is used as a transmitter and the second transceiver 620 is used as areceiver in FIG. 6 .

The first transceiver 610 includes a DM 612 b to apply probabilisticshaping to a digital signal 611 including binary data. A selector 612 ais employed to select the desired entropy. A labeler 614 is operativelycoupled to the DM 612 b to perform bit to symbol mapping. A firstencoder 613 b is operatively coupled to the labeler 614 to apply forwarderror correction (FEC) to the digital signal, and a selector 613 a isemployed to select the desired FEC code and/or code rate. The encodeddigital signal is then sent to a mapper 615 that is configured to mapbits into symbols. The first transceiver 610 also includes a digitalfilter 616 b to apply Nyquist shaping to the digital signal after themapper 615, and a digital to analog converter (DAC) 617 is thenconfigured to convert the digital signal into an analog signal. Betweenthe mapper 615 and the digital filter 616 b, overhead 619 is insertedinto the digital signal. In addition, a selector 616 a is also employedto select the desired Nyquist shaping scheme. An intensity modulator 618then modulates the analog signal for optical transmission in the fiberchannel 640.

The second transceiver 620 includes an analog to digital converter (ADC)621 to convert the analog signal received from the fiber channel 640into a digital signal, and a digital signal processor (DSP) 622 b isemployed to process the digital signal (e.g., recovering the signal). Inaddition, overhead information 629 is also retrieved and used insubsequent processing. The overhead information is sent to a reader 622a to find out the scheme of the Nyquist shaping that is used in thereceived signal and facilitate the DSP 622 b to recover the signal. Theoverhead information 629 is also sent to a second reader 623 a toretrieve the scheme of the FEC coding and facilitate a decoder 623 b toinverse decode the FEC codes. Furthermore, the overhead information 629is employed by a reader 624 a to find out the entropy information andfacilitate an inverse DM 624 b to perform inverse probabilistic shapingso as to recover the binary data 625. Between the DSP 622 b and thedecoder 623 b, a mapper 628 is employed to map symbol to bits. Inaddition, between the decoder 623 b and the inverse DM 624 b, an inverselabeler 626 is employed to perform inverse labeling.

The monitor 630 is configured to monitor the status of the fiber channel640 and then transmit the status information (e.g., OSNR or chromaticdispersion level) to the first transceiver 610. The transmission betweenthe monitor 630 and the first transceiver 610 can be conducted via asignal 635 formatted according to, for example, TCP/IP protocol.

Upon receiving the status information, the first transceiver 610 adjustsone or more operation parameters so as to optimize the transmission inthe fiber channel 640. As described herein, the first transceiver 610can adjust one or more of the following parameters: the number of bitsper symbol via the DM 612 b, the code rate of FEC via the first encoder613 b, and the ROF of Nyquist shaping via the digital filter 616 b.

In some implementations, the configuration of the first transceiver 610can be represented by three parameters: the number of bits per symbol(also referred to as entropy), the FEC code rate, and the ROF of theNyquist shaping. In some implementations, the configuration informationcan be represented in the format (entropy, code rate, ROF) and can befurther encoded in the signal as an option-indicator to facilitate thereceiver to retrieve information in the received signals.

In some embodiments, for a given capacity, other parameters of the firsttransceiver 610 can be determined as following. In these embodiments,the performances of M-PAM formats are compared under the same capacity,which can be defined as C=H(p)−m(1−R), where H(p) represents the entropyof the PS-MPAM, R is the FEC code rate, m=log₂(M), and M is the order ofthe PAM modulation.

For illustrative purposes only, three different capacities areconsidered here. In one example, the capacity is 2.7 b/s and PS is notused, and then the code rate can be 0.9, i.e. (3, 0.9) in the format of(entropy, code rate). In another example, the capacity is 2.4 b/s, thepossible options can be (3, 0.8) and (2.7, 0.9). In yet another example,the capacity is 2.1 b/s, and the options can be (3, 0.7), (2.7, 0.8),and (2.4, 0.9). In these examples, three different PS schemes have anentropy of 2.4, 2.7, and 3, respectively. There are also three FECcoding schemes having a code rate of 0.7, 0.8, and 0.9, respectively.Also for illustrative purposes only, three Nyquist shaping schemes canbe used, resulting in 18 configurations in the format of (entropy, coderate, ROF).

On the receiving end, the second transceiver 620 has three types ofinverse PS schemes corresponding to the three PS schemes in the firsttransceiver 610. Similarly, the second transceiver 620 also has threetypes of FEC decoding schemes in the decoder 623 and three types ofmatched filter schemes in the DSP 622. Because 18 differentconfigurations exist, at least 5 bits overhead are used as the indicatorand encoded in the signal send to the second transceiver 620.

Once the second transceiver 620 detects the indicator, the secondtransceiver 620 switches the DSP 622 b to the corresponding ROF value,switches the decoder 623 b to the corresponding code rate for decoding,and switches the DM 624 b to the corresponding entropy for inverse PS.

In some implementations, the system 600 can be employed to construct adata center network. In these implementations, for each configuration,the BER vs. OSNR curve can be measured. FIG. 7 shows BER as a functionof OSNR under different transmission configurations, according to anembodiment. Once the curves in FIG. 7 are obtained and a target BERthreshold is given (e.g., 1e⁻¹²), a user can select the (entropy, coderate, ROF) curve that provides the highest capacity at a certainmeasured OSNR value. In some embodiments, such selection can beautomatically implemented by a controller. In some embodiments, the usercan manually select the desired curve.

In some embodiments, an agile chart with a format of (OSNR, entropy,code rate, ROF) can be obtained. In the application of data centernetworks, the OSNR can be monitored and sent to the transmitter foradaptation according to the agile chart. The receiver is then switchedto the corresponding options by the option-indicator symbols sent by thetransmitter. As a result, a robust and high capacity data center networkcan be built.

More specifically, the agile chart can be produced based on the curvesshown in FIG. 7 . Out of several BER vs. OSNR curves in cases ofdifferent (entropy, code rate, ROF) combinations, one can find matchedcurves that can offer below-target BER performance at certain OSNR. Fromthese matched curves, one can then choose the (entropy, code rate, ROF)combinations that can offer the highest capacity. If there are more thantwo combinations that can offer the highest capacity and also meet theBER performance at certain OSNR, one can then choose the one that hasthe lowest power consumption. The power consumptions of DM, FEC coding,and Nyquist shaping can vary along with different combinations ofentropy, FEC code rate, and ROF. The agile chart can also include thepower consumption of each (entropy, code rate, ROF) combination.

FIG. 8 shows BER as a function of OSNR in optical communications viaPAM-8 using different PS schemes (i.e., Maxwell-Boltzmann andexponential distributions), according to an embodiment. FIG. 8 alsocompares the two PS distributions (labeled “Exp.-PS LDPC decoded” and“MB-PS LDPC decoded”) with the uniform distribution (labeled “UniformLDPC decoded”). In addition, the performance of LDPC coding is alsoillustrated. In FIG. 8 , solid lines represent the BER performance ofLDPC coded schemes, and dashed lines are BER performances withoutdecoding. The significant improvement due to LDPC and exponentialdistribution can be readily observed in FIG. 8 .

FIG. 9 shows BERs of optical communications as a function ofsignal-to-noise ratio (SNR) using different code rates of low-densityparity-check (LDPC) codes, according to an embodiment. It can be seenthat all the PS distribution schemes outperform the uniform distributionscheme, and the optimal performance is achieved when the code rate isabout 0.8.

FIGS. 10A-10C show frequency responses of neighboring wavelengthdivision multiplexing (WDM) channels using different roll-off factors(ROFs) of Nyquist shaping over the neighboring channels, according to anembodiment. In FIG. 10A, the left channel has an ROF of 1 and the secondchannel has an ROF of 0.1. In FIG. 10B, the two channels have the sameROF of 1. In FIG. 10C, the two channels have the same ROF of 0.1. Thebaud rate for each channel is set at 25 Gbaud, the sample rate is 4samples/symbol, and the channel spacing is 50 GHz. It can be seen fromFIGS. 10A-10C that a smaller ROF tends to achieve better spectralefficiency with a lower inter-channel crosstalk.

FIGS. 11A and 11B show BER performances at different ROFs usingLDPC-coded uniform distribution and PS distribution, respectively,according to an embodiment. In both situations, a smaller value of ROFcan lead to the frequency response of a rectangular shape, therebyimproving the spectral efficiency, and at the same time improving theBER performance for the same SNR.

While various embodiments have been described and illustrated herein, avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications arepossible. More generally, all parameters, dimensions, materials, andconfigurations described herein are meant to be examples and the actualparameters, dimensions, materials, and/or configurations will dependupon the specific application or applications for which the disclosureis used. It is to be understood that the foregoing embodiments arepresented by way of example only and that other embodiments may bepracticed otherwise than as specifically described and claimed.Embodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

Also, various concepts may be embodied as one or more methods, of whichan example has been provided. The acts performed as part of the methodmay be ordered in any suitable way. Accordingly, embodiments may beconstructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

As used herein, a “module” can be, for example, any assembly and/or setof operatively-coupled electrical components associated with performinga specific function, and can include, for example, a memory, aprocessor, electrical traces, optical connectors, software (stored andexecuting in hardware) and/or the like.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

What is claimed is:
 1. A method, comprising: applying, to a modulateddigital signal, a forward error correction (FEC) including a low-densityparity-check (LDPC) to produce a coded digital signal; applying Nyquistshaping to the coded digital signal to generate a filtered digitalsignal; and transmitting a representation of the filtered digital signalin an optical communication channel via a dense wavelength divisionmultiplexing (DWDM) scheme.
 2. The method of claim 1, furthercomprising: modulating a digital signal via pulse amplitude modulation(PAM) to generate the modulated digital signal.
 3. The method of claim1, further comprising: converting the filtered digital signal into ananalog signal, the representation of the filtered digital signal beingthe analog signal.
 4. The method of claim 1, wherein the FEC includes ahard decision FEC.
 5. The method of claim 1, wherein the FEC includes asoft decision FEC.
 6. The method of claim 1, further comprisingadjusting a code rate associated with the FEC based on a status of theoptical communication channel.
 7. The method of claim 1, wherein theapplying the Nyquist shaping to the coded digital signal includesapplying the Nyquist shaping at a roll-off factor (ROF) substantiallyequal to or less than 0.5.
 8. The method of claim 1, further comprising:in response to a chromatic dispersion level of the optical communicationchannel being greater than a predetermined value, decreasing a code rateassociated with the FEC; and in response to the chromatic dispersionlevel of the optical communication channel being less than thepredetermined value, increasing a code rate associated with the FEC. 9.The method of claim 1, further comprising: in response to an opticalsignal to noise ratio (OSNR) associated with the optical communicationchannel being greater than a predetermined value, increasing a code rateassociated with the FEC; and in response to the optical signal to noiseratio (OSNR) associated with the optical communication channel beingless than the predetermined value, decreasing the code rate associatedwith the FEC.
 10. A non-transitory computer readable storage mediumstoring data representing software executable by a computer, thesoftware including instruction to: apply, to a modulated digital signal,a forward error correction (FEC) to produce a coded digital signal;apply Nyquist shaping to the coded digital signal to generate a filtereddigital signal; and transmit a representation of the filtered digitalsignal in an optical communication channel via a dense wavelengthdivision multiplexing (DWDM) scheme.
 11. The non-transitory computerreadable storage medium of claim 10, wherein the software furtherincludes instructions to: modulate a digital signal via a pulseamplitude modulation (PAM) to generate the modulated digital signal. 12.The non-transitory computer readable storage medium of claim 10, whereinthe software further includes instructions to: convert the filtereddigital signal into an analog signal, the representation of the filtereddigital signal being the analog signal.
 13. The non-transitory computerreadable storage medium of claim 10, wherein the software furtherincludes instructions to: in response to a chromatic dispersion level ofthe optical communication channel being greater than a predeterminedvalue, decrease a code rate associated with the FEC; and in response tothe chromatic dispersion level of the optical communication channelbeing less than the predetermined value, increase a code rate associatedwith the FEC.
 14. The non-transitory computer readable storage medium ofclaim 10, wherein the software further includes instructions to: inresponse to an optical signal to noise ratio (OSNR) associated with theoptical communication channel being greater than a predetermined value,increase a code rate associated with the FEC; and in response to theoptical signal to noise ratio (OSNR) associated with the opticalcommunication channel being less than the predetermined value, decreasethe code rate associated with the FEC.
 15. The non-transitory computerreadable storage medium of claim 10, wherein the software furtherincludes instructions to: apply probabilistic shaping to the modulateddigital signal prior to applying the FEC.
 16. An apparatus, comprising:an encoder configured to apply a forward error correction (FEC) to amodulated digital signal to generate a coded digital signal; a digitalfilter operatively coupled to the encoder and configured to applyNyquist shaping to the coded digital signal to generate a filtereddigital signal; and a digital to analog converter (DAC) operativelycoupled to the digital filter, the DAC configured to send arepresentation of the filtered digital signal into an opticalcommunication channel.
 17. The apparatus of claim 16, further comprisinga modulator operatively coupled to the encoder and configured to encodebinary data into a digital signal via pulse amplitude modulation (PAM)to generate the modulated digital signal.
 18. The apparatus of claim 16,wherein the DAC is further configured to convert the filtered digitalsignal into an analog signal, the representation of the filtered digitalsignal being the analog signal.
 19. The apparatus of claim 16, furthercomprising: a controller operatively coupled to the digital filter andconfigured to: receive information representing at least one of anoptical signal to noise ratio (OSNR) or a chromatic dispersion level ofthe optical communication channel measured during transmission of therepresentations of the filtered digital signal, and cause the digitalfilter to change a code rate associated with the FEC based on theinformation.
 20. The apparatus of claim 16, wherein the digital filterhas an adjustable roll-off factor (ROF).